Report of the fit

Fit summary

Description: PV19 version x, parameters for NNLL. Trying the parameters that gave chi2 = 1.65708 for replica 0 when minimised with ceres. Minuit with the same parameters, starting from the same fitcofig, didn’t converge.
Minimiser: ceres
Random seed: 1234
Maximum values allowed for q_T / Q: 0.2
Cut on the error function: 2.8
Parameterisation: PV19x
Initial parameters fluctuations: True
Explicit formula:

f_{\rm NP}(x,\zeta, b_T)= \Biggl( \frac{1-\lambda}{1 + g_1(x) b_T^2/4} + \lambda \exp \left(-g_{1B}(x) b_T^2 / 4 \right)\Biggr) \exp\left[- g_2 \log\left(\frac{\zeta}{Q_0^2}\right) b_T^2/4 - g_{2B} \log\left(\frac{\zeta}{Q_0^2}\right) b_T^4/4 \right]g_1(x) = \frac{N_1}{x\sigma} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha}\right)}{2 \sigma^2} \right]g_{1B}(x) = \frac{N_{1B}}{x\sigma_B} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha_B}\right)}{2 \sigma_B^2} \right]Q_0^2 = 1\;{\rm GeV}^2 t_0 prescription: True

g_2	N_1	\alpha	\sigma	\lambda	N_{1B}	\alpha_B	\sigma_B	g_{2B}
0.005144	0.68535248	0.21943481	0.3329461	0.66627605	0.0387879	0.075758463	0.34845635	0.019224141

Theory summary

Collinear PDF set: MMHT2014nlo68cl member 0
Collinear FF set: DSS14_NLO_PiSum member 0
b^* prescription: bstarmin
Perturbative order: NNLL
Reference value of the fine-structure constant: \alpha(Q = 91.1876\;{\rm GeV}) = 0.00776578395589 (running True)

Global statistical estimators

N_{rep} = 200
\chi_{0}^2 = 1.6571
\chi_{mean}^2 = 1.6392
\langle\chi^2\rangle \pm \sigma_{\chi^2} = 1.6893 \pm 0.0455
\langle E \rangle \pm \sigma_{E} = 2.5699 \pm 0.1394

Parameters

Parameter	Central replica	Average over replicas	Fixed
g_2	-0.09141059	-0.07516749 \pm 0.02324989	False
N_1	5.3603904	13.82973829 \pm 54.00740774	False
\alpha	1.0686624	2.09075861 \pm 5.98685056	False
\sigma	0.93749188	0.86044179 \pm 0.26526407	False
\lambda	0.49349918	0.50479593 \pm 0.07450152	False
N_{1B}	0.040693304	0.03976956 \pm 0.22640261	False
\alpha_B	0.052748277	0.25774191 \pm 1.26648474	False
\sigma_B	0.56928194	1.94596686 \pm 24.52534851	False
g_{2B}	0.034354286	0.03215853 \pm 0.01056618	False

Fit properties

Global $\chi^2$ distribution — Global \chi^2 distribution

$\alpha$ distribution — \alpha distribution

$\sigma$ distribution — \sigma distribution

$\lambda$ distribution — \lambda distribution

$N_{1B}$ distribution — N_{1B} distribution

$\alpha_B$ distribution — \alpha_B distribution

$\sigma_B$ distribution — \sigma_B distribution

$g_{2B}$ distribution — g_{2B} distribution

Table of \chi^2’s

Central-replica \chi^2’s:
Experiment	Number of points	\chi_{D}^2	\chi_{\lambda}^2	\chi^2
E605_Q_7_8	7	0.4814	0.0307	0.5121
E605_Q_8_9	8	0.9948	0.0176	1.0124
E605_Q_10.5_11.5	10	0.494	0.1396	0.6336
E288_200_Q_4_5	4	0.9291	0.8595	1.7885
E288_200_Q_5_6	5	2.3107	0.3547	2.6654
E288_200_Q_6_7	6	0.7947	0.2112	1.0059
E288_200_Q_7_8	7	0.9887	0.032	1.0206
E288_200_Q_8_9	8	0.7359	0.0059	0.7419
E288_300_Q_4_5	4	0.7784	0.3426	1.121
E288_300_Q_5_6	5	1.3997	0.1	1.4997
E288_300_Q_6_7	6	1.042	0.0398	1.0818
E288_300_Q_7_8	7	0.3439	0.0425	0.3864
E288_300_Q_8_9	8	0.3919	0.0384	0.4303
E288_400_Q_5_6	5	0.9446	0.001	0.9456
E288_400_Q_6_7	6	0.5281	0.0068	0.5349
E288_400_Q_7_8	7	0.2499	0.0139	0.2637
E288_400_Q_8_9	8	0.5613	0.0126	0.574
E288_400_Q_11_12	11	0.5749	0.0068	0.5817
E288_400_Q_12_13	12	0.5394	0.0113	0.5507
E288_400_Q_13_14	12	0.3455	0.0363	0.3817
STAR_510	7	1.192	0.0136	1.2056
CDF_RunI	25	0.6522	0.1484	0.8006
CDF_RunII	26	1.2759	0.0074	1.2833
D0_RunI	12	0.6652	0.0018	0.667
D0_RunII	5	0.9114	0.2907	1.2022
D0_RunIImu	3	0.1197	0.0844	0.2041
LHCb_7TeV	7	1.945	0.8427	2.7877
LHCb_8TeV	7	1.9245	1.453	3.3775
LHCb_13TeV	7	1.4927	0.2893	1.782
CMS_7TeV	4	2.8928	0	2.8928
CMS_8TeV	4	1.4845	0.1782	1.6627
ATLAS_7TeV_y_0_1	6	6.9545	1.0911	8.0455
ATLAS_7TeV_y_1_2	6	4.9261	0.4825	5.4086
ATLAS_7TeV_y_2_2.4	6	1.8076	0.0099	1.8176
ATLAS_8TeV_y_0_0.4	6	4.7783	0.9776	5.756
ATLAS_8TeV_y_0.4_0.8	6	6.6974	1.5469	8.2443
ATLAS_8TeV_y_0.8_1.2	6	4.3581	0.6689	5.027
ATLAS_8TeV_y_1.2_1.6	6	2.9433	0.4249	3.3682
ATLAS_8TeV_y_1.6_2	6	2.5563	0.2696	2.8259
ATLAS_8TeV_y_2_2.4	6	1.2834	0.1619	1.4453
ATLAS_8TeV_Q_46_66	4	0.7685	0.0368	0.8053
ATLAS_8TeV_Q_116_150	8	1.1501	0.0073	1.1574
Total	319	-	-	1.6571

Mean-replica \chi^2’s:
Experiment	Number of points	\chi_{D}^2	\chi_{\lambda}^2	\chi^2
E605_Q_7_8	7	0.632	0.0898	0.7218
E605_Q_8_9	8	1.2311	0.048	1.2791
E605_Q_10.5_11.5	10	0.3645	0.1015	0.466
E288_200_Q_4_5	4	0.4534	0.4421	0.8956
E288_200_Q_5_6	5	1.3314	0.2707	1.6021
E288_200_Q_6_7	6	0.5796	0.1765	0.7562
E288_200_Q_7_8	7	0.9051	0.0334	0.9385
E288_200_Q_8_9	8	0.9342	0.0128	0.9469
E288_300_Q_4_5	4	0.5336	0.16	0.6935
E288_300_Q_5_6	5	1.1461	0.0595	1.2056
E288_300_Q_6_7	6	0.9439	0.0265	0.9704
E288_300_Q_7_8	7	0.326	0.033	0.359
E288_300_Q_8_9	8	0.2817	0.0393	0.321
E288_400_Q_5_6	5	1.0811	0.0171	1.0982
E288_400_Q_6_7	6	0.6129	0.0299	0.6427
E288_400_Q_7_8	7	0.2957	0.0462	0.3419
E288_400_Q_8_9	8	0.7447	0.0408	0.7856
E288_400_Q_11_12	11	0.839	0.0141	0.8531
E288_400_Q_12_13	12	0.8667	0.0173	0.884
E288_400_Q_13_14	12	0.8895	0.066	0.9555
STAR_510	7	1.1469	0.0372	1.1841
CDF_RunI	25	0.5739	0.1421	0.716
CDF_RunII	26	1.2356	0.006	1.2416
D0_RunI	12	0.6384	0.0007	0.6391
D0_RunII	5	1.0845	0.2943	1.3788
D0_RunIImu	3	0.022	0.0333	0.0554
LHCb_7TeV	7	1.682	0.8471	2.5291
LHCb_8TeV	7	1.8199	1.3821	3.202
LHCb_13TeV	7	1.3368	0.2691	1.6059
CMS_7TeV	4	2.8768	0	2.8768
CMS_8TeV	4	1.5098	0.1835	1.6933
ATLAS_7TeV_y_0_1	6	6.9378	1.0929	8.0307
ATLAS_7TeV_y_1_2	6	4.8183	0.4907	5.3091
ATLAS_7TeV_y_2_2.4	6	1.6825	0.01	1.6924
ATLAS_8TeV_y_0_0.4	6	4.7797	1.0131	5.7928
ATLAS_8TeV_y_0.4_0.8	6	6.5292	1.5932	8.1224
ATLAS_8TeV_y_0.8_1.2	6	4.3571	0.6881	5.0452
ATLAS_8TeV_y_1.2_1.6	6	2.9724	0.4409	3.4133
ATLAS_8TeV_y_1.6_2	6	2.4292	0.2746	2.7039
ATLAS_8TeV_y_2_2.4	6	1.1482	0.1534	1.3016
ATLAS_8TeV_Q_46_66	4	0.716	0.0522	0.7682
ATLAS_8TeV_Q_116_150	8	1.1316	0.0063	1.1379
Total	319	-	-	1.6392

Average-over-replicas \chi^2’s:
Experiment	Number of points	\chi_{D}^2	\chi_{\lambda}^2	\chi^2
E605_Q_7_8	7	0.4556 \pm 0.2212	0.159 \pm 0.2208	0.6146 \pm 0.1527
E605_Q_8_9	8	1.0508 \pm 0.2761	0.1109 \pm 0.1499	1.1617 \pm 0.2573
E605_Q_10.5_11.5	10	0.4775 \pm 0.2324	0.1831 \pm 0.2711	0.6606 \pm 0.2267
E288_200_Q_4_5	4	0.5964 \pm 1.195	1.0654 \pm 1.1838	1.6617 \pm 0.4361
E288_200_Q_5_6	5	2.123 \pm 0.6806	0.4521 \pm 0.6138	2.5751 \pm 0.3591
E288_200_Q_6_7	6	0.6674 \pm 0.384	0.283 \pm 0.3339	0.9504 \pm 0.2252
E288_200_Q_7_8	7	0.8673 \pm 0.2562	0.1206 \pm 0.1695	0.9879 \pm 0.2174
E288_200_Q_8_9	8	0.6849 \pm 0.1217	0.0712 \pm 0.0809	0.7561 \pm 0.1038
E288_300_Q_4_5	4	0.5264 \pm 0.7277	0.5038 \pm 0.6447	1.0302 \pm 0.2686
E288_300_Q_5_6	5	1.1632 \pm 0.4169	0.2684 \pm 0.3878	1.4317 \pm 0.3136
E288_300_Q_6_7	6	0.8485 \pm 0.3641	0.1685 \pm 0.2666	1.017 \pm 0.2918
E288_300_Q_7_8	7	0.2259 \pm 0.2243	0.142 \pm 0.231	0.3679 \pm 0.1665
E288_300_Q_8_9	8	0.3352 \pm 0.1639	0.1136 \pm 0.1777	0.4488 \pm 0.0864
E288_400_Q_5_6	5	0.7287 \pm 0.4086	0.1561 \pm 0.2214	0.8847 \pm 0.3408
E288_400_Q_6_7	6	0.4005 \pm 0.3474	0.11 \pm 0.1457	0.5106 \pm 0.3249
E288_400_Q_7_8	7	0.1753 \pm 0.2838	0.1047 \pm 0.1499	0.2799 \pm 0.244
E288_400_Q_8_9	8	0.5189 \pm 0.1827	0.0846 \pm 0.1097	0.6035 \pm 0.1553
E288_400_Q_11_12	11	0.5344 \pm 0.1127	0.0435 \pm 0.0574	0.5779 \pm 0.1089
E288_400_Q_12_13	12	0.5238 \pm 0.0829	0.0482 \pm 0.0655	0.572 \pm 0.0699
E288_400_Q_13_14	12	0.3349 \pm 0.1037	0.0767 \pm 0.0835	0.4116 \pm 0.1145
STAR_510	7	1.0669 \pm 0.2009	0.1136 \pm 0.1867	1.1806 \pm 0.0986
CDF_RunI	25	0.63 \pm 0.174	0.1903 \pm 0.171	0.8203 \pm 0.0467
CDF_RunII	26	1.2715 \pm 0.2155	0.0572 \pm 0.0721	1.3287 \pm 0.2078
D0_RunI	12	0.6294 \pm 0.1128	0.0654 \pm 0.0867	0.6947 \pm 0.0725
D0_RunII	5	0.6399 \pm 0.6421	0.4921 \pm 0.5654	1.132 \pm 0.28
D0_RunIImu	3	-0.3292 \pm 0.5872	0.5219 \pm 0.5419	0.1926 \pm 0.2952
LHCb_7TeV	7	1.8249 \pm 0.7541	1.0155 \pm 0.7196	2.8404 \pm 0.2052
LHCb_8TeV	7	1.9658 \pm 0.9316	1.526 \pm 0.8742	3.4918 \pm 0.3644
LHCb_13TeV	7	1.4009 \pm 0.447	0.3664 \pm 0.4275	1.7673 \pm 0.0982
CMS_7TeV	4	2.9017 \pm 0.0488	0.0 \pm 0.0	2.9017 \pm 0.0488
CMS_8TeV	4	1.4179 \pm 0.2711	0.2564 \pm 0.2307	1.6742 \pm 0.1121
ATLAS_7TeV_y_0_1	6	6.9701 \pm 0.8299	1.1829 \pm 0.5859	8.153 \pm 0.5601
ATLAS_7TeV_y_1_2	6	4.9796 \pm 0.4804	0.5661 \pm 0.3526	5.5457 \pm 0.3456
ATLAS_7TeV_y_2_2.4	6	1.8507 \pm 0.1667	0.0299 \pm 0.0383	1.8806 \pm 0.1637
ATLAS_8TeV_y_0_0.4	6	4.9952 \pm 0.6953	1.0249 \pm 0.4628	6.0201 \pm 0.4915
ATLAS_8TeV_y_0.4_0.8	6	6.7879 \pm 0.7674	1.6129 \pm 0.6929	8.4007 \pm 0.3869
ATLAS_8TeV_y_0.8_1.2	6	4.3167 \pm 0.4064	0.6347 \pm 0.3148	4.9514 \pm 0.2649
ATLAS_8TeV_y_1.2_1.6	6	2.9257 \pm 0.3964	0.4608 \pm 0.3231	3.3865 \pm 0.2378
ATLAS_8TeV_y_1.6_2	6	2.6784 \pm 0.4567	0.3277 \pm 0.3152	3.0061 \pm 0.3298
ATLAS_8TeV_y_2_2.4	6	1.5619 \pm 0.6057	0.2441 \pm 0.217	1.806 \pm 0.5764
ATLAS_8TeV_Q_46_66	4	0.6044 \pm 0.3186	0.2233 \pm 0.319	0.8277 \pm 0.0999
ATLAS_8TeV_Q_116_150	8	1.0685 \pm 0.1686	0.1089 \pm 0.1584	1.1774 \pm 0.0561
Total	319	-	-	1.6893 \pm 0.0455